SINGLE EVENT. “Complex multicellularity has only arisen twice, once in animals and once in vascular plants. One might add fungi to the list, although the number of fungal cell types is not large, and there is some question as to whether multicellularity was ancestral to the phylogenetic group that contains animals, fungi, and slime molds.”
http://www.pnas.org/content/112/33/10278.full